A shock-capturing meshless method for solving the one-dimensional Saint-Venant equations on a highly variable topography
The Saint-Venant equations are numerically solved to simulate free surface flows in one dimension. A Riemann solver is needed to compute the numerical flux for capturing shocks and flow discontinuities occurring in flow situations such as hydraulic jump, dam-break wave propagation, or bore wave prop...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IWA Publishing
2023-07-01
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| Series: | Journal of Hydroinformatics |
| Subjects: | |
| Online Access: | http://jhydro.iwaponline.com/content/25/4/1235 |
| Summary: | The Saint-Venant equations are numerically solved to simulate free surface flows in one dimension. A Riemann solver is needed to compute the numerical flux for capturing shocks and flow discontinuities occurring in flow situations such as hydraulic jump, dam-break wave propagation, or bore wave propagation. A Riemann solver that captures shocks and flow discontinuities is not yet reported to be implemented within the framework of a meshless method for solving the Saint-Venant equations. Therefore, a wide range of free surface flow problems cannot be simulated by the available meshless methods. In this study, a shock-capturing meshless method is proposed for simulating one-dimensional (1D) flows on a highly variable topography. The Harten–Lax–van Leer Riemann solver is used for computing the convective flux in the proposed meshless method. Spatial derivatives in the Saint-Venant equations and the reconstruction of conservative variables for flux terms are computed using a weighted least square approximation. The proposed method is tested for various numerically challenging problems and laboratory experiments on different flow regimes. The proposed highly accurate shock-capturing meshless method has the potential to be extended to solve the two-dimensional (2D) shallow water equations without any mesh requirements.
HIGHLIGHTS
A shock-capturing meshless method is presented for solving the 1D Saint-Venant equations on a highly variable topography.;
The points are irregularly distributed along the channel to define minute topographical features.;
The meshless method can accurately capture shocks and flow discontinuity in open channel flows.; |
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| ISSN: | 1464-7141 1465-1734 |